# A simple log question

#### rogerfreak

This question should be easy to most people here and need some help on this question.

3log25 - log34 + log2(log39)

My answer to this question is:
= 3log25 - log34 + log2(log9/log3)
= log2125 - log34 + log22
= log2125 - log34 + 1
= (log125 / log2) - (log4 / log3) + 1
= 6.703924778

However the correct answer give is 6.335, which means my answer is wrong. Can somebody tell me what's wrong with my answer and what should I do to get the correct answer? Thanks :)

Last edited:

#### Zurtex

Homework Helper
These steps you have made do not make any sense:

$$\log_2 \log_2 9 \Rightarrow \log_2 \left( \frac{\log 9}{\log 3} \right) \Rightarrow \log_2 2$$

#### rogerfreak

opps...sorry. i had a typo in my post. edited it

it should be:
$$\log_2 \log_3 9 \Rightarrow \log_2 \left( \frac{\log 9}{\log 3} \right) \Rightarrow \log_2 2$$

but i still cannot solve this equation. :(

#### Zurtex

Homework Helper
Well in that case your reduction of the logs is perfectly correct and your approximation to the number in decimal places is also correct. The number is about:

6.7039247775191721694119040597826488189953228988...

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